Kaplan-Meier survival analysis

The Kaplan-Meier estimator is a nonparametric way to estimate the survival function, S(t). That is the probability of surviving beyond a given time, t, from time-to-event data that includes 'censored' cases. At each event time, the estimate is updated. You take the subjects still at risk, subtract those who just had the event, and multiply the result forward (a 'product-limit'). The output is a step-shaped curve. It shows survival over the follow-up, and lets you compare groups with the log-rank test. The method makes two key assumptions. First, censoring is non-informative: people who leave the study are not systematically different in prognosis. Second, survival is independent across individuals. The median survival, where the curve crosses 50%, is the standard summary. The mean survival is rarely used, because it needs the curve to reach zero.

Last reviewed: June 22, 2026

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